Question

A study of recent records of car accidents revealed that average proportion of drivers who were distracted by their phones at the time of accident was 35% with a margin error of 9%. If we want a margin of error of 4%, how many records needs to be studied? (All data analysis is done at the 95% confidence level).

Answer 1

Answer:

At least 547 records need to be studied.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$, and a confidence interval $1-\alpha$, we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$.

And the margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence interval

So $\alpha = 0.05$, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$, so $z = 1.96$.

In this problem, we have that:

$M = 0.04, p = 0.35$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.35*0.65}{n}}$

$0.04\sqrt{n} = 0.93486$

$\sqrt{n} = 23.37$

$n = 546.2275$

At least 547 records need to be studied.